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Winning streak threshold

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A trader makes $100$ independent trades, and each wins with probability $\frac{1}{2}$ . To approximate the probability of at least $60$ wins with a normal distribution, a continuity correction is applied. What $z$ -value is used?

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Hint

At least $60$ wins means the boundary sits halfway between $59$ and $60$ .

Solution

The number of wins has mean $100 \times \frac{1}{2} = 50$ .
Its standard deviation is $100 \times \frac{1}{2} \times \frac{1}{2} = 5$ .
With continuity correction, the event is at least $59.5$ on the continuous scale.
The $z$ -value is $(59.5 - 50) \div 5 = 1.9$ .

Answer: $1.9$

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